Lead as its own luminescent sensor

Lead (II) in polar organic solvents such as acetone, acetonitrile, and propylenecarbonate with excess bromide generates the highly luminescent lead-halide cluster Pb(4)Br(11)(3)(-). This in situ sensor does not rely on a host-guest relationship and, thus, is intrinsically selective and sensitive, allowing for the detection of lead at nanomolar concentrations. The cluster's emission maximum and relaxation kinetics are temperature dependent and indicate a close spacing of intralead and intracluster electronic energy levels.     

Degree-one maps between hyperbolic 3-manifolds with the same volume limit

Suppose that are degree-one maps between closed hyperbolic 3-manifolds with

Then, our main theorem, Theorem 2, shows that, for all but finitely many , is homotopic to an isometry. A special case of our argument gives a new proof of Gromov-Thurston's rigidity theorem for hyperbolic 3-manifolds without invoking any ergodic theory. An example in §3 implies that, if the degree of these maps is greater than 1, the assertion corresponding to our theorem does not hold.

     

High-angular-momentum states in cold Rydberg gases

Cold, dense Rydberg gases produced in a cold-atom trap are investigated using spectroscopic methods and time-resolved electron counting. Optical excitation on the discrete Rydberg resonances reveals long-lasting electron emission from the Rydberg gas ( >20 ms). Our observations are explained by lm-mixing collisions between Rydberg atoms and slow electrons that lead to the population of long-lived high-angular-momentum Rydberg states. These atoms thermally ionize slowly and with large probabilities.     

Letter: Particle-like Behaviour of Some Bianchi Cosmologies: A Fundamental Unity in Nature?

We show that the equations of evolution of someBianchi cosmologies with equation of state p = (0 1) are formallysimilar to the equations of motion of a classical particle under the actionof suitably chosen potential functions. This appears topoint to a fundamental unity in Nature.     

Unified study and transport properties of simple metals

The resistivity, thermoelectric power at the melting points and temperature variation of resistivity of the liquid alkali metals are studied with local Heine-Abarenkov and the modified Ashcroft pseudopotentials. The parameters of the model potentials are obtained from a unified study of the static and dynamic properties of the metals. The effect of different dielectric function and structure factor on the transport properties is discussed. It is shown that the simple modified Ashcroft pseudopotential reproduces the result fairly well except for Li and Cs.     

Efficient proton-templated synthesis of 18- to 38-membered tetraimino(amino)diphenol macrocyclic ligands: structural features and spectroscopic properties

A whole range of Robson-type tetraiminodiphenol macrocyclic ligands have been prepared as their perchlorate salts [H4L](ClO4)2 in high yield (ca. 90%) by a single-step [2 + 2] condensation reaction between 4-methyl(or tert-butyl)-2,6-diformyl(or diacyl)phenols and alpha,omega-diaminoalkanes (C2-C12) in the presence of acetic acid and NaClO4. The reduction of these 18- to 38-membered macrocyclic salts with NaBH4 have afforded corresponding tetraaminodiphenol macrocycles H2L'. The X-ray crystal structures of two of the tetraiminodiphenol macrocycles with the C2 and C4 lateral chains have been determined, and the optimized configurations for all of the macrocycles have been obtained by molecular mechanics calculations. The macrocycles have been characterized by elemental analysis and by IR, absorption, emission, and NMR spectroscopic study. The protonated tetraiminodiphenol macrocycles exhibit strong fluoroscence in methanol, acetonitrile, and nitromethane and undergo quenching when treated with triethylamine. The neutral macrocycles H2L, isolated by treating [H4L](ClO4)2 with excess of triethylamine, lack luminescence, as do the reduced tetraaminodiphenol macrocycles H2L'. The hydrolytic cleavage of [H4L](ClO4)2 has been studied.     

On modules of finite projective dimension over complete intersections

Recently Avramov and Miller proved that over a local complete intersection ring in characteristic 0$">, a finitely generated module has finite projective dimension if for some 0$"> and for some 0$">, being the frobenius map repeated times. They used the notion of ``complexity' and several related theorems. Here we offer a very simple proof of the above theorem without using ``complexity' at all.